20 February 2008
10 February 2008
Kernels and distances are closely related. Given a kernel K(x,z), this induces an RKHS H such that K(x,z)=
On the other hand, we also know how to turn distance metrics into kernels. If (X,d) is a metric space (i.e., X is a space and d is a metric on X), then K(x,z)=exp(-d(x,z)) is positive semi-definite when x,z are drawn from X.
Now, there are three questions that arise. The first is: in the distance->kernel setting, what does the RKHS "look like." I think the sense here is that it's basically the same as the RKHS induced by the Gaussian kernel: it's an infinite-dimensional feature space where different dimensions look like distances to some point. In practice, this "some point" is going to be one of the training points.
The second question follows the fact that we can iterate this construction. One way to ask this is: if we use a kernel to induce a distance, then use this distance to introduce a new kernel, what does this new kernel look like. Or, alternatively, if we have a distance, kernelize it to induce a new distance, then what does this distance look like. I don't have a good intuitive sense for the answer to any of these. Obviously it's straightforward to write out what these things look like, but that doesn't directly give me a sense of what's going on.
The final question is a bit "off topic" from the above two, but still relevant. There's been a lot of work in kernels for discrete data, like strings. The most popular string subsequence kernel is based on counting how many subsequences match between two strings, down-weighted by the length of the subsequences. It's well known, and recognized in string kernel papers, that a kernel of the form K(x,z) = 1-ned(x,z), where ned is a normalized string edit distance is not a valid kernel. However, from what we know about distance metrics, K(x,z) = exp(-sed(x,z)) should be a valid kernel. Yet I'm not aware of this being used anywhere. Is there any reason why? The reason I ask is because it's a much more intuitive than the subsequence kernel, which I only have a vague sense about.
03 February 2008
The friend I crashed with while attending SODA is someone I've known since we were five years old. (Incidentally, there's actually someone in the NLP world who I've actually known from earlier...small world.) Anyway, the friend I stayed with is just finishing med school at UCSF and will soon be staying there for residency. His specialty is neurosurgery, and his interests are in neural pathologies. He spent some time doing research on Alzheimer's disease, effectively by studying mice (there's something I feel sort of bad about finding slightly amusing about mice with Alzheimer's disease). Needless to say, in the process of doing research, he made nearly daily use out of PubMed. (For those of you who don't know, PubMed is like the ACL anthology, but with hundreds of thousands of papers, with new ones being added by the truckload daily, and will a bunch of additional things, like ontologies and data sets.)
There are two things I want to talk about regarding PubMed. I think both of these admit very interesting problems that we, as NLPers, are qualified to tackle. I think the most important thing, however, is opening and maintaining a wide channel of communication. There seems to be less interaction between people who do (for instance) bio-medical informatics (we have a fairly large group here) and what I'll term as mainstream NLPers. Sure, there have been BioNLP workshops at ACLs, but I really think that both communities would be well-served to interact more. And for those of you who don't want to work on BioNLP because it's "just a small domain problem", let me assure you: it is not easy... don't think of it in the same vein as a true "sublanguage" -- it is quite broad.
I suppose I should give a caveat that my comments below are based on a sample size of one (my friend), so it may not be totally representative. But I think it generalizes.
Search in PubMed, from what I've heard, is good in the same ways that web search is good and bad in the same ways that web search is bad. It is good when you know what you're looking for (i.e., you know the name for it) and bad otherwise. One of the most common sorts of queries that my friend wants to do is something like "show me all the research on proteins that interact in some way with XXX in the context of YYY" where XXX is (eg) a gene and YYY is (eg) a disease. The key is that we don't know which proteins these are and so it's hard to query for them directly. I know that this is something that the folks at Penn (and probably elsewhere) are working on, and I get the impression that a good solution to this problem would make lots and lots of biologists much happier (and more productive). One thing that was particularly interesting, however, is that he was pretty averse to using structured queries like the one I gave above. He effectively wants to search for "XXX YYY" and have it realize that XXX is a gene, YYY is a disease, and that it's "obvious" that what he wants is proteins that interact with (or even, for instance, pathways that contain) XXX in the context of disease YYY. On the other hand, if YYY were another gene, then probably he's be looking for diseases or pathways that are regulated by both XXX and YYY. It's a bit complex, but I don't think this is something particularly beyond our means.
The other thing I want to talk about is summarization. PubMed actually archives a fairly substantial collection of human-written summaries. These fall into one of two categories. The first, called "systematic reviews" are more or less what we would think of as summaries. However, they are themselves quite long and complex. They're really not anything like sentence extracts. The second, called "meta analyses" are really not like summaries at all. In a meta analysis, an author will consider a handful of previously published papers on, say, the effects of smoking on lifespan. He will take the data and results published in these individual papers, and actually do novel statistical analyses on them to see how well the conclusions hold.
From a computational perspective, the automatic creation of meta analyses would essentially be impossible, until we have machines that can actually run experiments in the lab. "Systematic reviews", on the other hand, while totally outside the scope of our current technology, are things we could hope to do. And they give us lots of training data. There are somewhere around ten to forty thousand systematic reviews on PubMed, each about 20 pages long, and each with references back to papers, almost all of which are themselves in PubMed. Finding systematic reviews older than a few years ago (when the began being tagged explicitly) has actually sprouted a tiny cottage industry. And PubMed nicely makes all of their data available for download, without having to crawl, something that makes life much easier for us.
My friend warns that it might not be a good idea to use all systematic reviews, but only those from top journals. (They tend to be less biased, and better written.) However, in so far as I don't think we'd even have hope of getting something as good as a systematic review from the worst journal in the world, I'm not sure this matters much. Maybe all it says is that for evaluation, we should be careful to evaluate against the top.
Now, I should point out that people in biomedical informatics have actually been working on the summarization problem too. From what I can tell, the majority of effort there is on rule-based systems that build on top of more rule-based systems that extract genes, pathways and relations. People at the National Library of Medicine, Rindflesch and Fiszman, use SemRep to do summarization, and they have tried applying it to some medical texts. Two other people that I know are doing this kind of work are Kathy McKeown and Greg Whalen, both at Columbia. The Columbia group has access to a medically informed NLP concept extractor called MedLEE, which gives them a leg up on the low-level processing details. If you search for 'summarization medical OR biomedical' in GoogleScholar, you'll get a raft of hits (~9000).
Now, don't get me wrong -- I'm not saying that this is easy -- but for summarization folks who are constantly looking for "natural artifacts" of their craft, this is an enormous repository.